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Excitonic Quasi-particles

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Semiconductor Optics 1

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Abstract

In this chapter we illustrate the quasi-particle properties of excitons, which are the bound states of electron–hole pair excitations in semiconductors and insulators. We will develop the concept of Wannier excitons to describe the wavefunction and dispersion relation of these excitations. We also introduce triplet excitons which are the (mostly dark) partners of the singlet ones. Then we discuss modifications of the simple exciton model due the phonon-related polarization of the crystalline lattice and introduce the exciton finestructure due to various exchange interactions. We close with an introduction to excitonic molecules (biexcitons) and charged excitons (trions).

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Author information

Authors and Affiliations

  1. Institute of Applied Physics, Karlsruhe Institute of Technology, Karlsruhe, Baden-WĂĽrttemberg, Germany

    Heinz Kalt & Claus F. Klingshirn

Authors
  1. Heinz Kalt
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  2. Claus F. Klingshirn
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Correspondence to Heinz Kalt .

Problems

Problems

20.1

Calculate the Rydberg energy and the Bohr radius of excitons for some important semiconductors. The required material parameters can be found in Appendix C or, e.g., in [82L1]. Compare these with the experimentally determined binding energies and lattice constants, respectively.

20.2

How many (different) exciton states can be constructed in a semiconductor with zinc-blende \((T_{d})\) structure for the principal quantum numbers \(n_{{\mathrm {B}}}=1, 2\) and 3?

20.3

Compare the magnitude of the relative splitting between 2s and 2p states in a hydrogen atom (what are the physical reasons?) with the 2s–2p splitting of excitons.

20.4

Plot the Rydberg series of an idealized three- and two-dimensional exciton and indicate the oscillator strengths.

20.5

Calculate the (combined) density of states in the continuum of a three- and a two-dimensional exciton in the effective-mass approximation. Multiply by the corresponding Sommerfeld enhancement factor.

20.6

Find in the literature data for the binding energies of the exciton ground state and of the higher states (i.e. \({{n}}_{{\mathrm {B}}}{{S}}\) or \({{n}}_{{\mathrm {B}}}{{P}}\) states with \({{n}}_{{\mathrm {B}}} \ge 2\)), e.g., for GaAs, ZnO, CuCl and Cu\(_{2}\)O and determine for which ones the 1S state fits into the hydrogen series with higher states.

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Kalt, H., Klingshirn, C.F. (2019). Excitonic Quasi-particles. In: Semiconductor Optics 1. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-24152-0_20

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